Notes
three congruent rectangles vi solution

Solution to the Three Congruent Rectangles VI Puzzle

Solution by Area of a Triangle and Congruent Triangles

Consider the diagram labelled as above. Triangles $A H G$ and $A H F$ share the base $A H$, and as $F G$ is parallel to $A H$, the points $F$ and $G$ have the same perpendicular distance to $A H$, so triangles $A H G$ and $A H F$ have the same area.

Since the rectangles are congruent, line segments $C F$ and $B H$ have the same length, so so do $C B$ and $F H$. Therefore $A F$ is parallel to $B D$. Since also $A H$ and $D C$ have the same length then triangles $D B E$ and $A F E$ are congruent.

The white regions therefore have the same area as triangle $A B H$, which comprises one half of one of the rectangles and so one sixth of the design.